Abstract
We consider two applications of the factorization of infrared dynamics in QED and gravity. The first is a redefinition of the Lorentz transformations that makes them commute with supertranslations. The other is the process of particle creation near a black hole horizon. For the latter we show that the emission of soft particles factors out of the S-matrix in the fixed-background approximation and to leading order in the soft limit. The factorization is implemented by dressing the incoming and outgoing asymptotic states with clouds of soft photons and soft gravitons. We find that while the soft photon cloud has no effect, the soft graviton cloud induces a phase shift in the Bogolyubov coefficients relating the incoming and outgoing modes. However, the flux of outgoing particles, given by the absolute value of the Bogolyubov coefficient, is insensitive to this phase.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. Bloch and A. Nordsieck, Note on the radiation field of the electron, Phys. Rev. 52 (1937) 54 [INSPIRE].
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
T.D. Lee and M. Nauenberg, Degenerate systems and mass singularities, Phys. Rev. 133 (1964) B1549 [INSPIRE].
V. Chung, Infrared divergence in quantum electrodynamics, Phys. Rev. 140 (1965) B1110 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. I. Classical currents, J. Math. Phys. 9 (1968) 315.
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. II. Mass-shell singularities of Green’s functions, Phys. Rev. 173 (1968) 1527 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. III. Asymptotic states and reduction formulas, Phys. Rev. 174 (1968) 1882 [INSPIRE].
T.W.B. Kibble, Coherent soft-photon states and infrared divergences. IV. The scattering operator, Phys. Rev. 175 (1968) 1624 [INSPIRE].
P.P. Kulish and L.D. Faddeev, Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745 [Teor. Mat. Fiz. 4 (1970) 153] [INSPIRE].
A. Strominger, Lectures on the infrared structure of gravity and gauge theory, arXiv:1703.05448 [INSPIRE].
A. Strominger, Black hole information revisited, arXiv:1706.07143 [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Infrared quantum information, Phys. Rev. Lett. 119 (2017) 180502 [arXiv:1706.03782] [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Dressed infrared quantum information, Phys. Rev. D 97 (2018) 025007 [arXiv:1710.02531] [INSPIRE].
M. Mirbabayi and M. Porrati, Dressed hard states and black hole soft hair, Phys. Rev. Lett. 117 (2016) 211301 [arXiv:1607.03120] [INSPIRE].
R. Bousso and M. Porrati, Soft hair as a soft wig, Class. Quant. Grav. 34 (2017) 204001 [arXiv:1706.00436] [INSPIRE].
R. Bousso and M. Porrati, Observable supertranslations, Phys. Rev. D 96 (2017) 086016 [arXiv:1706.09280] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Soft hair on black holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].
S.W. Hawking, M.J. Perry and A. Strominger, Superrotation charge and supertranslation hair on black holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].
A. Averin, G. Dvali, C. Gomez and D. Lüst, Goldstone origin of black hole hair from supertranslations and criticality, Mod. Phys. Lett. A 31 (2016) 1630045 [arXiv:1606.06260] [INSPIRE].
C. Gomez and S. Zell, Black hole evaporation, quantum hair and supertranslations, Eur. Phys. J. C 78 (2018) 320 [arXiv:1707.08580] [INSPIRE].
B. Gabai and A. Sever, Large gauge symmetries and asymptotic states in QED, JHEP 12 (2016) 095 [arXiv:1607.08599] [INSPIRE].
D. Kapec, M. Perry, A.-M. Raclariu and A. Strominger, Infrared divergences in QED, revisited, Phys. Rev. D 96 (2017) 085002 [arXiv:1705.04311] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New symmetries of massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
D. Kapec, M. Pate and A. Strominger, New symmetries of QED, Adv. Theor. Math. Phys. 21 (2017) 1769 [arXiv:1506.02906] [INSPIRE].
H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
A. Strominger, On BMS invariance of gravitational scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
D. Christodoulou and S. Klainerman, The global nonlinear stability of the Minkowski space, Princeton University Press, Princeton, U.S.A. (1993) [INSPIRE].
M. Henneaux and C. Troessaert, BMS group at spatial infinity: the Hamiltonian (ADM) approach, JHEP 03 (2018) 147 [arXiv:1801.03718] [INSPIRE].
M. Henneaux and C. Troessaert, Asymptotic symmetries of electromagnetism at spatial infinity, JHEP 05 (2018) 137 [arXiv:1803.10194] [INSPIRE].
M. Henneaux and C. Troessaert, Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity, JHEP 07 (2018) 171 [arXiv:1805.11288] [INSPIRE].
S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
S.W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
F.H.J. Cornish, Energy and momentum in general relativity — III. The total energy, momentum and angular momentum of an isolated finite system generating gravitational waves, Proc. Roy. Soc. Lond. A 286 (1965) 270.
J. Ware, R. Saotome and R. Akhoury, Construction of an asymptotic S matrix for perturbative quantum gravity, JHEP 10 (2013) 159 [arXiv:1308.6285] [INSPIRE].
S. Choi, U. Kol and R. Akhoury, Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations, JHEP 01 (2018) 142 [arXiv:1708.05717] [INSPIRE].
S. Choi and R. Akhoury, BMS supertranslation symmetry implies Faddeev-Kulish amplitudes, JHEP 02 (2018) 171 [arXiv:1712.04551] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP 12 (2015) 094 [arXiv:1509.01406] [INSPIRE].
M. Campiglia, Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime, JHEP 11 (2015) 160 [arXiv:1509.01408] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1808.02987
At Kyoto University from 1 June to 31 August 2018. (Massimo Porrati)
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Javadinezhad, R., Kol, U. & Porrati, M. Comments on Lorentz transformations, dressed asymptotic states and Hawking radiation. J. High Energ. Phys. 2019, 89 (2019). https://doi.org/10.1007/JHEP01(2019)089
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)089